Magnetic activity of six young solar analogues II. Surface Differential Rotation from long-term photometry

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Abstract
The present paper is the second of a series dedicated to the study of the magnetic activity in a selected sample of young solar analogues. The sample includes five single G0-G5V stars with ages between $\simeq$130 Myr and 700 Myr: EK Dra, π 1 UMa, HN Peg, k1 Cet and BE Cet. In this study we also include the Pleiades-age ($\simeq$130 Myr) K0V star DX Leo. Our analysis is based on high precision photometric observations carried out as part of The Sun in Time project, aimed at a multiwavelength study of stars with solar-like global properties, but with different ages and thus at different stages of evolution. In the first paper of this series we presented the photometric observations and determined the existence of starspot cycles and their correlation with the global stellar properties. In the present paper we investigate the surface differential rotation (SDR). The periodogram analysis of the photometric data time series has allowed us to determine the rotational periods and to derive the following results: i) all the selected stars show variations of the rotational period. Such variations are definitely periodic and in phase with the starspot cycle for BE Cet and DX Leo. They are likely periodic and in phase also for π 1 UMa, EK Dra and HN Peg, but still need confirmation. By analogy with the solar butterfly diagram, the rotational period variations are interpretable in terms of surface differential rotation, that is, they are attributable to the existence of active latitude belts migrating during the activity cycle on a differentially rotating star; ii) BE Cet, π 1 UMa and EK Dra show a solar-like pattern of SDR, that is the rotational period steadily decreases along the activity cycle, jumping back to higher values at the beginning of the next cycle; on the contrary, DX Leo, k1 Cet and HN Peg show an antisolar pattern; iii) the amplitude of the rotational period variations shows a power law dependence on the rotational period similar to that found in previous studies. Contrary to theoretical predictions, the cycle length is not correlated to the Dynamo number, it is indeed positively correlated to the SDR amplitude. More precisely, stars tend to concentrate along three different branches with the cycle length increasing with increasing $\Delta\Omega$/Ω. Moreover, we found that the SDR amplitude changes from cycle to cycle, which is reminiscent of a wave of excess rotation propagating in latitude; iiii) the apparently different solar and antisolar behaviours are probably due to different inclinations of the stellar rotation axis under which the star is seen. The long-term photometry of the young single star LQ Hya, although not included in the initial project, is also used in the present analysis to enlarge the investigated sample. We determined for LQ Hya three different starspot cycles and an antisolar pattern of SDR.